Editing Interest rate

{{Short description|Percentage of a sum of money charged for its use}}
{{Finance sidebar}}
{{Macroeconomics sidebar}}
An '''interest rate''' is the amount of [[interest]] due per period, as a proportion of the amount lent, [[Deposit (finance)|deposited]], or borrowed (called the [[principal sum]]). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed.

The '''annual interest rate''' is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually [[rate of return#Annualization|annualized]].

The interest rate has been characterized as "an index of the preference . . . for a dollar of present [income] over a dollar of future income".<ref>{{cite book |last1=Fisher |first1=Irving |title=The Rate of Interest: Its Nature, Determination and Relation to Economic Phenomena |date=1907 |publisher=The MacMillan Company |location=New York |isbn=1578987458 |page=3 |url=https://archive.org/details/rateofinterestit00fishuoft/page/n29/mode/2up}}</ref> The borrower wants, or needs, to have money sooner, and is willing to pay a fee—the interest rate—for that privilege.

==Influencing factors==
Interest rates vary according to:
* the government's directives to the [[central bank]] to accomplish the government's goals
* the [[currency]] of the principal sum lent or borrowed
* the term to maturity of the [[investment]]
* the perceived default probability of the borrower
* [[supply and demand]] in the market
* the amount of collateral
* special features like call provisions
* reserve requirements
* compensating balance

as well as other factors.

==Example==
A company borrows [[financial capital|capital]] from a bank to buy assets for its business. In return, the bank charges the company interest. (The lender might also require rights over the new assets as [[collateral (finance)|collateral]].)

A bank will use the capital deposited by individuals to make loans to their clients. In return, the bank should pay interest to individuals who have deposited their capital. The amount of interest payment depends on the interest rate and the amount of capital they deposited.

==Related terms==
''Base rate'' usually refers to the annualized [[effective interest rate]] offered on overnight deposits by the central bank or other monetary authority.{{citation needed|date=August 2013}}

The ''[[annual percentage rate]]'' (APR) may refer either to a nominal APR or an effective APR (EAPR). The difference between the two is that the EAPR accounts for fees and compounding, while the nominal APR does not.

The ''annual equivalent rate'' (AER), also called the effective annual rate, is used to help consumers compare products with different compounding frequencies on a common basis, but does not account for fees.

A ''discount rate''<ref>{{Cite web |title=Discount Rate Defined: How It's Used by the Fed and in Cash-Flow Analysis |url=https://www.investopedia.com/terms/d/discountrate.asp |access-date=2023-05-08 |website=Investopedia |language=en}}</ref> is applied to calculate [[present value]].

For an interest-bearing security, ''[[Nominal yield|coupon rate]]'' is the ratio of the annual coupon amount (the coupon paid per year) per unit of par value, whereas ''[[current yield]]'' is the ratio of the annual coupon divided by its current market price. ''[[Yield to maturity]]'' is a bond's expected [[internal rate of return]], assuming it will be held to maturity, that is, the discount rate which equates all remaining cash flows to the investor (all remaining coupons and repayment of the par value at maturity) with the current market price.

Based on the banking business, there are deposit interest rate and loan interest rate.

Based on the relationship between supply and demand of market interest rate, there are fixed interest rate and floating interest rate.

==Monetary policy==
''Interest rate targets'' are a vital tool of [[monetary policy]] and are taken into account when dealing with variables like [[investment]], [[inflation]], and [[unemployment]]. The [[central bank]]s of countries generally tend to reduce interest rates when they wish to increase investment and consumption in the country's [[economy]]. However, a low interest rate as a macro-economic policy can be [[risk management|risky]] and may lead to the creation of an [[economic bubble]], in which large amounts of investments are poured into the real-estate market and stock market. In [[Developed country|developed economies]], interest-rate adjustments are thus made to keep inflation within a target range for the health of [[economic activities]] or cap the interest rate concurrently with [[economic growth]] to safeguard economic [[momentum]].<ref>{{cite news |url= https://www.reuters.com/article/usa-debt-inflation-idUSN1E7711UC20110802 |work=Reuters |title=INSIGHT-Mild inflation, low interest rates could help economy |date=2 August 2011}}</ref><ref>{{cite journal |last1=Sepehri |first1=Ardeshir |author-link2 = Saeed Moshiri |last2=Moshiri |first2=Saeed |year=2004 |title=Inflation-Growth Profiles Across Countries: Evidence from Developing and Developed Countries |journal=International Review of Applied Economics |volume=18 |issue=2 |pages=191–207 |doi=10.1080/0269217042000186679 |s2cid=154979402 }}</ref><ref>{{cite web|url=http://www.imf.org/external/pubs/ft/fandd/2003/06/pdf/inflatio.pdf|title=Inflation : Finding the right balance|website=Imf.org|access-date=8 January 2018}}</ref><ref>{{cite web|url=http://www.imf.org/external/pubs/ft/fandd/2003/06/index.htm|title=Finance & Development, June 2003 - Contents|work=Finance and Development – F&D}}</ref><ref>{{cite web|url=http://www.imf.org/external/pubs/ft/fandd/2010/03/basics.htm|title=Finance & Development, March 2010 – Back to Basics|work=Finance and Development – F&D}}</ref>

==History==
[[Image:German bank interest rates from 1967 to 2003 grid.svg|thumb|right|Germany experienced deposit interest rates from 14% in 1973 down to almost 2% in 2003.]]
In the past two centuries, interest rates have been variously set either by national governments or central banks. For example, the Federal Reserve [[federal funds rate]] in the United States has varied between about 0.25% and 19% from 1954 to 2008, while the [[Bank of England]] base rate varied between 0.5% and 15% from 1989 to 2009,<ref>moneyextra.com [http://www.moneyextra.com/dictionary/interest-rate-history-003455.php Interest Rate History] {{webarchive|url=https://web.archive.org/web/20081016004207/http://www.moneyextra.com/dictionary/Interest-rate-history-003455.php |date=2008-10-16 }}. Retrieved 2008-10-27</ref><ref>{{cite news |url= http://news.bbc.co.uk/1/hi/business/7925620.stm |title=UK interest rates lowered to 0.5% |work=BBC News |date=5 March 2009}}</ref> and Germany experienced rates close to 90% in the 1920s down to about 2% in the 2000s.<ref>{{Harv|Homer|Sylla|Sylla|1996|loc=p. 509}}</ref><ref>[[Bundesbank]]. [http://www.bundesbank.de/statistik/statistik_zeitreihen.en.php?lang=en&open=&func=row&tr=SU0021 BBK – Statistics – Time series database] {{webarchive|url=https://web.archive.org/web/20090212210639/http://www.bundesbank.de/statistik/statistik_zeitreihen.en.php?lang=en&open=&func=row&tr=SU0021 |date=2009-02-12 }}. Retrieved 2008-10-27</ref> During an attempt to tackle spiraling [[hyperinflation]] in 2007, the Central Bank of [[Zimbabwe]] increased interest rates for borrowing to 800%.<ref>worldeconomies.co.uk [http://www.worldeconomies.co.uk/03102007-382.html Zimbabwe currency revised to help inflation] {{webarchive|url=https://web.archive.org/web/20090211062924/http://www.worldeconomies.co.uk/03102007-382.html |date=2009-02-11 }}</ref>

The [[prime rate|interest rates on prime credits]] in the late 1970s and early 1980s were far higher than had been recorded – higher than previous US peaks since 1800, than British peaks since 1700, or than Dutch peaks since 1600; "since modern capital markets came into existence, there have never been such high long-term rates" as in this period.<ref>{{Harv|Homer|Sylla|Sylla|1996|loc=p. 1}}</ref>

Before modern capital markets, there have been accounts that savings deposits could achieve an annual return of at least 25% and up to as high as 50%.<ref>{{cite book |last1=Ellis |first1=William |last2=Dawes |first2=Richard |title=Lessons on the Phenomena of Industrial Life: And the Conditions of Industrial Success |year=1857 |publisher=Groombridge |pages=iii–iv |url={{GBurl|JXhHAAAAYAAJ|pg=PR3}}}}</ref>

==Reasons for changes==
[[File:Interest rates.webp|thumb|350px|Prime rate floats about 3% above the federal funds rate.
{{legend-line|#80699B dotted 3px|Credit card interest rates}}
{{legend-line|#4572A7 dotted 3px|[[Auto loan]] interest rate 48 months new autos}}
{{legend-line|#3D96AE solid 3px|[[Prime rate]] }}
{{legend-line|#BD10E0 solid 3px|[[Government bond|10 year Treasury bond]]}}
{{legend-line|#AA4643 solid 3px|[[United States Consumer Price Index]]}}
{{legend-line|#89A54E solid 3px|[[Federal funds rate]] }}
]]
* '''Political short-term gain''': Lowering interest rates can give the economy a short-run boost. Under normal conditions, most economists think a cut in interest rates will only give a short term gain in economic activity that will soon be offset by inflation. The quick boost can influence elections. Most economists advocate independent central banks to limit the influence of politics on interest rates.
* '''Deferred consumption''': When [[money]] is loaned the [[lender]] delays spending the money on [[Consumption (economics)|consumption]] goods. Since according to [[time preference]] theory people prefer goods now to goods later, in a free market there will be a positive interest rate.
* '''Inflationary expectations''': Most economies generally exhibit [[inflation]], meaning a given amount of money buys fewer goods in the future than it will now. The borrower needs to compensate the lender for this.
* '''Alternative investments''': The lender has a choice between using his money in different investments. If he chooses one, he forgoes the returns from all the others. Different investments effectively compete for funds.
* '''Risks of investment''': There is always a risk that the borrower will go [[Bankruptcy|bankrupt]], abscond, die, or otherwise [[Default (finance)|default]] on the loan. This means that a lender generally charges a [[risk premium]] to ensure that, across his investments, he is compensated for those that fail.
* '''Liquidity preference''': People prefer to have their resources available in a form that can immediately be exchanged, rather than a form that takes time to realize.
* '''Taxes''': Because some of the gains from interest may be subject to [[Tax|taxes]], the lender may insist on a higher rate to make up for this loss.
* '''Banks''': [[Bank|Banks]] can tend to change the interest rate to either slow down or speed up economy growth. This involves either raising interest rates to slow the economy down, or lowering interest rates to promote economic growth.<ref>Commonwealth Bank [https://www.mywealth.commbank.com.au/learn/choosing-investments/why-do-interest-rates-change Why do Interest Rates Change?] {{webarchive|url=https://web.archive.org/web/20140226001350/https://www.mywealth.commbank.com.au/learn/choosing-investments/why-do-interest-rates-change |date=2014-02-26 }}</ref>
* '''Economy''': Interest rates can fluctuate according to the status of the economy. It will generally be found that if the economy is strong then the interest rates will be high, if the economy is weak the interest rates will be low.

==Real versus nominal==
{{Main|Real versus nominal value (economics)}}
{{Further|Fisher equation}}
The [[nominal interest rate]] is the rate of interest with no adjustment for [[inflation]].

For example, suppose someone deposits $100 with a bank for one year, and they receive interest of $10 (before tax), so at the end of the year, their balance is $110 (before tax). In this case, regardless of the rate of inflation, the [[nominal interest rate]] is 10% ''per annum'' (before tax).

The [[real interest rate]] measures the growth in [[real versus nominal value (economics)|real value]] of the loan plus interest, taking [[inflation]] into account. The repayment of principal plus interest is measured in [[real versus nominal value (economics)|real terms]] compared against the [[buying power]] of the amount at the time it was borrowed, lent, deposited or invested.

If inflation is 10%, then the $110 in the account at the end of the year has the same purchasing power (that is, buys the same amount) as the $100 had a year ago. The [[real interest rate]] is zero in this case.

The real interest rate is given by the [[Fisher equation]]:
: <math>r = \frac{1+i}{1+p}-1\,\!</math>
where ''p'' is the inflation rate.
For low rates and short periods, the [[linear approximation]] applies:
: <math>r \approx i-p\,\!</math>

The Fisher equation applies both ''[[ex ante]]'' and ''[[ex post]]''. ''Ex ante'', the rates are projected rates, whereas ''ex post'', the rates are historical.

==Market rates==
There is a [[Market (economics)|market]] for investments, including the [[money market]], [[bond market]], [[stock market]], and [[currency market]] as well as retail [[bank]]ing.

Interest rates reflect:
* The [[risk-free interest rate|risk-free cost of capital]]
* Expected [[inflation]]
* [[Risk premium]]
* [[Transaction cost]]s

===Inflationary expectations===
According to the theory of [[rational expectations]], borrowers and lenders form an expectation of [[inflation]] in the future. The acceptable nominal interest rate at which they are willing and able to borrow or lend includes the [[real interest rate]] they require to receive, or are willing to pay, plus the rate of [[inflation]] they expect. Under behavioral expectations, the formation of expectations deviates from rational expectations due to cognitive limitations and information processing costs. Agents may exhibit myopia (limited attention) to certain economic variables, form expectations based on simplified heuristics, or update their beliefs more gradually than under full rationality. These behavioral frictions can affect monetary policy transmission and optimal policy design.<ref>{{cite journal |doi=10.1016/j.jfs.2023.101151 |title=Optimal monetary policy under bounded rationality |journal=Journal of Financial Stability |volume=67 |pages=101151 |year=2023 |last1=Benchimol |first1=Jonathan |last2=Bounader |first2=Lahcen |hdl=10419/212417 |url=http://www.imf.org/external/pubs/cat/longres.aspx?sk=47048 |hdl-access=free }}</ref>

===Risk===
The level of [[risk]] in investments is taken into consideration. [[volatility (finance)|Riskier]] investments such as [[share (finance)|shares]] and [[junk bond]]s are normally expected to deliver higher returns than safer ones like [[government bond]]s.

The additional return above the risk-free nominal interest rate which is expected from a risky investment is the [[risk premium]]. The risk premium an investor requires on an investment depends on the [[risk-neutral measure|risk preferences]] of the investor. Evidence suggests that most lenders are risk-averse.<ref>Benchimol, J., 2014. [https://ideas.repec.org/a/eee/reecon/v68y2014i1p39-56.html Risk aversion in the Eurozone], [[Research in Economics]], vol. 68, issue 1, pp. 39–56.</ref>

A '''maturity risk premium''' applied to a longer-term investment reflects a higher perceived risk of default.

There are four kinds of risk:
* [[repricing risk]]
* [[basis risk]]
* yield curve risk
* optionality

===Liquidity preference===
Most economic agents exhibit a [[liquidity preference]], defined as the propensity to hold [[cash]] or highly liquid assets over less [[Fungibility|fungible]] investments, reflecting both precautionary and transactional motives. Liquidity preference manifests in the yield differential between assets of varying maturities and convertibility costs, where cash provides immediate transaction capability with zero conversion costs. This preference creates a term structure of required returns, exemplified by the higher yields typically demanded for longer-duration assets. For instance, while a 1-year loan offers relatively rapid convertibility to cash, a 10-year loan commands a greater liquidity premium. However, the existence of deep secondary markets can partially mitigate illiquidity costs, as evidenced by US [[Treasury bond]]s, which maintain significant liquidity despite longer maturities due to their unique status as a safe asset and the associated financial sector stability benefits.<ref>{{cite journal |doi=10.1086/666589 |title=The Aggregate Demand for Treasury Debt |journal=Journal of Political Economy |volume=120 |issue=2 |pages=233–267 |year=2012 |last1=Krishnamurthy |first1=Arvind |last2=Vissing-Jorgensen |first2=Annette |url=http://www.minneapolisfed.org/research/SR/SR410.pdf }}</ref><ref>{{cite journal |doi=10.1016/j.jfineco.2015.09.001 |title=The impact of Treasury supply on financial sector lending and stability |journal=Journal of Financial Economics |volume=118 |issue=3 |pages=571–600 |year=2015 |last1=Krishnamurthy |first1=Arvind |last2=Vissing-Jorgensen |first2=Annette }}</ref>

===A market model===
A basic interest rate pricing model for an asset is

: <math>i_n = i_r + p_e + r_p + l_p\,\!</math>

where

: ''i<sub>n</sub>'' is the nominal interest rate on a given investment
:''i<sub>r</sub>'' is the risk-free return to capital
: ''i*<sub>n</sub>'' is the nominal interest rate on a short-term risk-free liquid bond (such as U.S. [[treasury bill]]s).
: ''r<sub>p</sub>'' is a risk premium reflecting the length of the investment and the likelihood the borrower will default
: ''l<sub>p</sub>'' is a liquidity premium (reflecting the perceived difficulty of converting the asset into money and thus into goods).
: ''p<sub>e</sub>'' is the expected inflation rate.

Assuming perfect information, ''p<sub>e</sub>'' is the same for all participants in the market, and the interest rate model simplifies to

: <math>i_n = i^*_n + r_p + l_p\,\!</math>

===Spread===
The ''spread'' of interest rates is the lending rate minus the deposit rate.<ref>[http://data.worldbank.org/indicator/FR.INR.LNDP Interest rate spread (lending rate minus deposit rate, %)] from [[World Bank]]. 2012</ref> This spread covers operating costs for banks providing loans and deposits. A ''negative spread'' is where a deposit rate is higher than the lending rate.<ref>[http://definitions.uslegal.com/n/negative-spread/ Negative Spread Law & Legal Definition], retrieved January 2013</ref>

==In macroeconomics==

===Output, unemployment and inflation===
Interest rates affect economic activity broadly, which is the reason why they are normally the main instrument of the [[monetary policies]] conducted by [[central bank]]s.<ref name=Blanchard>{{cite book |last1=Blanchard |first1=Olivier |last2=Amighini |first2=Alessia |last3=Giavazzi |first3=Francesco |title=Macroeconomics: a European perspective | chapter=Monetary policy:a summing up | date=2017 |publisher=Pearson |location=Harlow London New York Boston San Francisco Toronto Sydney Dubai Singapore Hong Kong Tokyo Seoul Taipei New Delhi Cape Town São Paulo Mexico City Madrid Amsterdam Munich Paris Milan |isbn=978-1-292-08567-8 |edition=3rd}}</ref> Changes in interest rates will affect firms' [[investment]] behaviour, either raising or lowering the [[opportunity cost]] of investing. Interest rate changes also affect [[asset prices]] like [[stock price]]s and [[Real estate appraisal|house prices]], which again influence households' [[Consumption (economics)|consumption]] decisions through a [[wealth effect]]. Additionally, international interest rate differentials affect exchange rates and consequently [[exports]] and [[imports]]. These various channels are collectively known as the [[monetary transmission mechanism]]. Consumption, investment and net exports are all important components of [[aggregate demand]]. Consequently, by influencing the general interest rate level, monetary policy can affect overall demand for goods and services in the economy and hence [[Output (economics)|output]] and [[employment]].<ref>{{cite web |title=Federal Reserve Board - Monetary Policy: What Are Its Goals? How Does It Work? |url=https://www.federalreserve.gov/monetarypolicy/monetary-policy-what-are-its-goals-how-does-it-work.htm |website=Board of Governors of the Federal Reserve System |access-date=16 September 2023 |language=en |date=29 July 2021}}</ref> Changes in employment will over time affect [[wage]] setting, which again affects [[pricing]] and consequently ultimately inflation. The relation between employment (or unemployment) and inflation is known as the [[Phillips curve]].<ref name=Blanchard/>

For economies maintaining a [[fixed exchange rate system]], determining the interest rate is also an important instrument of monetary policy as international [[Financial capital|capital]] flows are in part determined by interest rate differentials between countries.<ref>{{cite web |title=Fixed exchange rate policy |url=https://www.nationalbanken.dk/en/frequently-asked-questions/fixed-exchange-rate-policy |website=Nationalbanken |access-date=16 September 2023 |language=en}}</ref>

=== Interest rate setting in the United States===
[[Image:Federal funds effective rate 1954 to present.svg|thumb|right|375px|The effective federal funds rate in the US charted over more than half a century]]
The Federal Reserve (often referred to as 'the Fed') implements [[monetary policy]] largely by targeting the [[federal funds rate]] (FFR). This is the rate that banks charge each other for overnight loans of [[federal funds]], which are the reserves held by banks at the Fed. Until the [[2008 financial crisis]], the Fed relied on [[open market operations]], i.e. selling and buying securities in the open market to adjust the supply of reserve balances so as to keep the FFR close to the Fed's target.<ref name="OMO">{{cite web |title=Open Market Operations |url=https://www.federalreserve.gov/monetarypolicy/openmarket.htm |website=www.federalreserve.gov |publisher=Federal Reserve System |access-date=16 September 2023 |language=en |date=26 July 2023}}</ref> However, since 2008 the actual conduct of monetary policy implementation has changed considerably, the Fed using instead various administered interest rates (i.e.,  interest rates that are set directly by the Fed rather than being determined by the market forces of supply and demand) as the primary tools to steer short-term market interest rates towards the Fed's policy target.<ref>{{cite web |last1=Ihrig |first1=Jane |last2=Weinbach |first2=Gretchen C. |last3=Wolla |first3=Scott A. |title=Teaching the Linkage Between Banks and the Fed: R.I.P. Money Multiplier |url=https://research.stlouisfed.org/publications/page1-econ/2021/09/17/teaching-the-linkage-between-banks-and-the-fed-r-i-p-money-multiplier |website=research.stlouisfed.org |publisher=Federal Reserve Bank of St. Louis |access-date=16 September 2023 |language=en |date=September 2021}}</ref>

==Impact on savings and pensions==
[[Financial economist]]s such as [[:fr: Forum Mondial des Fonds de Pension|World Pensions Council (WPC)]] researchers have argued that durably low interest rates in most G20 countries will have an adverse impact on the [[funding]] positions of pension funds as "without returns that outstrip inflation, pension investors face the real value of their savings declining rather than ratcheting up over the next few years".<ref name="Reuters">{{Cite news|author=M. Nicolas J. Firzli quoted in Sinead Cruise |title= Zero Return World Squeezes Retirement Plans |url= http://uk.mobile.reuters.com/article/businessNews/idUKBRE8720T320120803  |work=Reuters with CNBC |date= 4 August 2012|access-date=5 Aug 2012 }}</ref> Current interest rates in [[savings account]]s often fail to keep up with the pace of inflation.<ref>{{Cite web|last=thesavingsguy|date=2021-11-16|title=Why You Can't Afford to use Savings Accounts for Saving - Ask The savings guy|url=https://www.askthesavingsguy.com/2021/11/16/why-you-cant-afford-to-use-savings-accounts-for-saving/,%20https://www.askthesavingsguy.com/2021/11/16/why-you-cant-afford-to-use-savings-accounts-for-saving/|url-status=live|archive-url=https://web.archive.org/web/20211116070622/https://www.askthesavingsguy.com/2021/11/16/why-you-cant-afford-to-use-savings-accounts-for-saving/|archive-date=2021-11-16|access-date=2021-11-18|language=en-US}}</ref>

From 1982 until 2012, most Western economies experienced a period of low inflation combined with relatively high returns on investments across all [[asset class]]es including government bonds. This brought a certain sense of complacency{{citation needed|date=April 2019}} amongst some pension [[actuarial]] consultants and [[regulator (economics)|regulators]], making it seem reasonable to use optimistic economic assumptions to calculate the [[present value]] of future pension liabilities.

==Mathematical note==
Because interest and inflation are generally given as percentage increases, the formulae above are [[linear approximation|(linear) approximations]].

For instance,

: <math>i_n = i_r + p_e\,\!</math>

is only approximate. In reality, the relationship is

: <math>(1 + i_n) = (1 + i_r)(1 + p_e)\,\!</math>

so

: <math>i_r = \frac {1 + i_n} {1 + p_e} - 1\,\!</math>
The two approximations, eliminating [[higher order terms]], are:
:<math>\begin{align}
(1+x)(1+y) &= 1+x+y+xy &&\approx 1+x+y\\
\frac{1}{1+x} &= 1-x+x^2-x^3+\cdots &&\approx 1-x
\end{align}</math>

The formulae in this article are exact if [[logarithmic unit]]s are used for relative changes, or equivalently if [[logarithm]]s of [[index (economics)|indices]] are used in place of rates, and hold even for large relative changes.

==Zero rate policy==
{{Main|Zero interest-rate policy}}

A so-called "zero interest-rate policy" (ZIRP) is a very low—near-zero—central bank target interest rate. At this [[Zero lower bound problem|zero lower bound]] the central bank faces difficulties with conventional monetary policy, because it is generally believed that market interest rates cannot realistically be pushed down into negative territory.

In the United States, the policy was used in 2008-2015 ([[2008 financial crisis]]) and 2020-2022 ([[COVID-19 pandemic]]).<ref>{{cite web |title=Federal Funds Effective Rate (FEDFUNDS) |url=https://fred.stlouisfed.org/series/FEDFUNDS |access-date=20 March 2025}}</ref>

==Negative nominal or real rates{{anchor|Negative interest rates}}==
''Nominal'' interest rates are normally positive, but not always. In contrast, ''real'' interest rates can be negative, when nominal interest rates are below inflation. When this is done via government policy (for example, via reserve requirements), this is deemed [[financial repression]], and was practiced by countries such as the United States and United Kingdom [[Aftermath of World War II|following World War II]] (from 1945) until the late 1970s or early 1980s (during and following the [[Post–World War II economic expansion]]).<ref>{{cite web|url=http://www.pimco.com/EN/Insights/Pages/The-Caine-Mutiny-Part-2.aspx|title=The Caine Mutiny Part 2 – PIMCO|author=William H. Gross|work=Pacific Investment Management Company LLC|access-date=2011-12-21|archive-date=2012-10-13|archive-url=https://web.archive.org/web/20121013181717/http://www.pimco.com/EN/Insights/Pages/The-Caine-Mutiny-Part-2.aspx|url-status=dead}}</ref><ref>{{cite web|url=http://www.imf.org/external/pubs/ft/fandd/2011/06/pdf/reinhart.pdf|title=Financial Repression Redux (Reinhart, Kirkegaard, Sbrancia June 2011)|website=Imf.org|access-date=8 January 2018}}</ref> In the late 1970s, [[United States Treasury security|United States Treasury securities]] with negative real interest rates were deemed {{anchor|certificate of confiscation}}''certificates of confiscation''.<ref>{{Cite news | last = Norris | first = Floyd | title = U.S. Bonds That Could Return Less Than Their Price |newspaper= [[The New York Times]] |date=28 October 2010 |url= https://www.nytimes.com/2010/10/29/business/economy/29norris.html}}</ref>

===On central bank reserves===
{{Main|Negative interest on excess reserves}}
A so-called "negative interest rate policy" (NIRP) is a negative (below zero) central bank target interest rate.

====Theory====
{{Main|Demurrage currency}}
Given the alternative of holding cash, and thus earning 0%, rather than lending it out, profit-seeking lenders will not lend below 0%, as that will guarantee a loss, and a bank offering a negative deposit rate will find few takers, as savers will instead hold cash.<ref>{{cite news |url= http://blogs.ft.com/maverecon/2009/05/negative-interest-rates-when-are-they-coming-to-a-central-bank-near-you/
|title=Negative interest rates: when are they coming to a central bank near you?
|date=7 May 2009
|first=Willem
|last=Buiter
|author-link=Willem Buiter
|work=[[Financial Times]] blog
}}</ref>

Negative interest rates have been proposed in the past, notably in the late 19th century by [[Silvio Gesell]].<ref name="mankiw">{{Cite news |url= https://www.nytimes.com/2009/04/19/business/economy/19view.html |title=It May Be Time for the Fed to Go Negative |work=The New York Times |first=N. Gregory |last=Mankiw |author-link=N. Gregory Mankiw |date=18 April 2009}}</ref> A negative interest rate can be described (as by Gesell) as a "tax on holding money"; he proposed it as the ''[[Demurrage currency|Freigeld]]'' (free money) component of his {{Lang|de|[[Freiwirtschaft]]}} (free economy) system. To prevent people from holding cash (and thus earning 0%), Gesell suggested issuing money for a limited duration, after which it must be exchanged for new bills; attempts to hold money thus result in it expiring and becoming worthless. Along similar lines, [[John Maynard Keynes]] approvingly cited the idea of a carrying tax on money,<ref name="mankiw" /> (1936, ''[[The General Theory of Employment, Interest and Money]]'') but dismissed it due to administrative difficulties.<ref name="wired">{{Cite magazine |title = Cash and the 'Carry Tax' |first = Declan |last = McCullagh |magazine = WIRED |access-date = 2011-12-21 |url = https://www.wired.com/politics/law/news/1999/10/32121 |archive-url=https://web.archive.org/web/20080617034453/https://www.wired.com/politics/law/news/1999/10/32121 |archive-date=17 June 2008 |date=27 October 1999}}</ref> More recently, a carry tax on currency was proposed by a [[Federal Reserve]] employee (Marvin Goodfriend) in 1999, to be implemented via magnetic strips on bills, deducting the carry tax upon deposit, the tax being based on how long the bill had been held.<ref name="wired" />

It has been proposed that a negative interest rate can in principle be levied on existing paper currency via a [[serial number]] lottery, such as randomly choosing a number 0 through 9 and declaring that notes whose serial number end in that digit are worthless, yielding an average 10% loss of paper cash holdings to hoarders; a drawn two-digit number could match the last two digits on the note for a 1% loss. This was proposed by an anonymous student of [[Greg Mankiw]],<ref name="mankiw" /> though more as a thought experiment than a genuine proposal.<ref>

See follow-up blog posts for discussion: "[http://gregmankiw.blogspot.com/2009/04/observations-on-negative-interest-rates.html Observations on Negative Interest Rates]", 19 April 2009;
"[http://gregmankiw.blogspot.com/2009/04/more-on-negative-interest-rates.html More on Negative Interest Rates]", 22 April 2009; "[http://gregmankiw.blogspot.com/2009/05/more-on-negative-interest-rates.html More on Negative Interest Rates]", 7 May 2009, all in [http://gregmankiw.blogspot.com/ Greg Mankiw's Blog: Random Observations for Students of Economics]</ref>

====Practice====
Both the [[European Central Bank]] starting in 2014 and the [[Bank of Japan]] starting in early 2016 pursued the policy on top of their earlier and continuing [[quantitative easing]] policies. The latter's policy was said at its inception to be trying to "change Japan's 'deflationary mindset.'" In 2016 [[#Negative interest on central bank reserves|Sweden, Denmark]] and Switzerland—not directly participants in the [[Euro]] currency zone—also had NIRPs in place.<ref>Nakamichi, Takashi, Megumi Fujikawa and Eleanor Warnock, [https://www.wsj.com/articles/bbank-of-japan-introduces-negative-interest-rates-1454040311 "Bank of Japan Introduces Negative Interest Rates" (possibly subscription-only)]{{Dead link|date=October 2022 |bot=InternetArchiveBot |fix-attempted=yes }}, Wall Street ''Journal'', January 29, 2016. Retrieved 2016-01-29.</ref>

Countries such as Sweden and Denmark have set negative interest on reserves—that is to say, they have charged interest on reserves.<ref>{{cite journal|last=Goodhart|first=C.A.E.|title=The Potential Instruments of Monetary Policy|date=January 2013|journal=Financial Markets Group Paper|issue=Special Paper 219|url=http://www2.lse.ac.uk/fmg/workingPapers/specialPapers/PDF/SP219.pdf|access-date=13 April 2013|at=9–10|publisher=London School of Economics|issn=1359-9151}}</ref><ref>{{cite journal|last=Blinder|first=Alan S.|title=Revisiting Monetary Policy in a Low-Inflation and Low-Utilization Environment|journal=Journal of Money, Credit and Banking|date=February 2012|volume=44|issue=Supplement s1|pages=141–146|doi=10.1111/j.1538-4616.2011.00481.x}}</ref><ref>{{cite web|last=Thoma|first=Mark|title=Would Lowering the Interest Rate on Excess Reserves Stimulate the Economy?|url=http://economistsview.typepad.com/economistsview/2012/08/would-lowering-the-interest-rate-on-excess-reserves-stimulate-the-economy.html|work=Economist's View|access-date=13 April 2013|date=August 27, 2012}}</ref><ref>{{cite web|last=Parameswaran|first=Ashwin|title=On The Folly of Inflation Targeting In A World Of Interest Bearing Money|url=http://www.macroresilience.com/2013/01/07/on-the-folly-of-inflation-targeting-in-a-world-of-interest-bearing-money/|work=Macroeconomic Resilience|access-date=13 April 2013|date=2013-01-07}}</ref>

In July 2009, Sweden's central bank, the [[Riksbank]], set its policy repo rate, the interest rate on its one-week deposit facility, at 0.25%, at the same time as setting its overnight deposit rate at −0.25%.<ref name="sweden-negative-repo-table">{{Cite web|url = http://www.riksbank.se/en/Interest-and-exchange-rates/Repo-rate-table/|title = Repo rate table|access-date = 21 August 2013|publisher = Sveriges Riksbank|archive-url = https://web.archive.org/web/20130205235742/http://www.riksbank.se/en/Interest-and-exchange-rates/Repo-rate-table/|archive-date = 5 February 2013|url-status = dead}}</ref> The existence of the negative overnight deposit rate was a technical consequence of the fact that overnight deposit rates are generally set at 0.5% below or 0.75% below the policy rate.<ref name="sweden-negative-repo-table" /><ref name=":0">{{Cite news |url= http://www.ft.com/cms/s/0/5d3f0692-9334-11de-b146-00144feabdc0.html |archive-url=https://ghostarchive.org/archive/20221210/http://www.ft.com/cms/s/0/5d3f0692-9334-11de-b146-00144feabdc0.html |archive-date=2022-12-10 |url-access=subscription |title=Bankers watch as Sweden goes negative |first1=Andrew |last1=Ward |first2=David |last2=Oakley |work=[[Financial Times]] |location =London |date=27 August 2009}}</ref> The Riksbank studied the impact of these changes and stated in a commentary report<ref>{{Cite web|url = http://www.riksbank.se/upload/Dokument_riksbank/Kat_publicerat/Ekonomiska%20kommentarer/2009/ek_kom_no11_09eng.pdf|title = The lower limit of the Riksbank's repo rate|date = 30 September 2009|publisher = Sveriges Riksbank|access-date = 21 August 2013|last1 = Beechey|first1 = Meredith|last2 = Elmér|first2 = Heidi}}</ref> that they led to no disruptions in Swedish financial markets.

===On government bond yields===
[[File:Ireland bond prices.webp|thumb|300px|Ireland bond prices, [[Inverted yield curve]] in 2011,<ref>[https://www.researchgate.net/figure/a-Irish-yield-curve-dynamics-around-2011-loan-amendments-b-Portuguese-yield-curve_fig2_342609297 Figure. Irish yield curve]</ref> And rates went negative after the [[European debt crisis]].
{{legend-line|#FF8200 solid 3px|15 year bond}}
{{legend-line|#009A44 solid 3px|10 year bond}}
{{legend-line|#88FA4E solid 3px|5 year bond}}
{{legend-line|#970E53 solid 3px|3 year bond}}
]]
During the [[European debt crisis]], government bonds of some countries (Switzerland, Denmark, Germany, Finland, the Netherlands and Austria) have been sold at negative yields. Suggested explanations include desire for safety and protection against the eurozone breaking up (in which case some eurozone countries might redenominate their debt into a stronger currency).<ref>{{cite news
|url=http://www.ft.com/intl/cms/s/0/bd22fe1c-d0f1-11e1-8957-00144feabdc0.html#axzz22TvqCmZa
|archive-url=https://ghostarchive.org/archive/20221210221256/https://www.ft.com/content/bd22fe1c-d0f1-11e1-8957-00144feabdc0#axzz22TvqCmZa
|archive-date=2022-12-10
|url-access=subscription
|url-status=live
|title=Schatz yields turn negative for first time
|date=18 July 2012
|first=Robin
|last=Wigglesworth
|work=[[Financial Times]]
|location=London
|access-date=2012-08-03
}}</ref>

===On corporate bond yields===

For practical purposes, [[Investor|investors]] and academics typically view the yields on government or quasi-government bonds guaranteed by a small number of the most creditworthy governments (United Kingdom, United States, Switzerland, EU, Japan) to effectively have negligible default risk. As financial theory would predict, investors and academics typically do not view non-government guaranteed corporate bonds in the same way. Most credit analysts value them at a spread to similar government bonds with similar duration, geographic exposure, and currency exposure. Through 2018 there have only been a few of these corporate bonds that have traded at negative nominal interest rates.
The most notable example of this was Nestle, some of whose AAA-rated bonds traded at negative nominal interest rate in 2015. However, some academics and investors believe this may have been influenced by volatility in the currency market during this period.

==See also==
* [[Forward rate]]
* [[Interest expense]]
* [[List of sovereign states by central bank interest rates]]
* [[Macroeconomics]]
* [[Rate of return]]
* [[Short-rate model]]
* [[Spot contract#Bonds and swaps|Spot rate]]

==Notes==
{{Reflist}}

==References==
* {{Cite book |title=A History of Interest Rates | first1 = Sidney | last1 = Homer | first2 = Richard Eugene | last2 = Sylla | first3 = Richard | last3 = Sylla |publisher=[[Rutgers University Press]] |year=1996 |isbn=978-0-8135-2288-3 |url=https://archive.org/details/historyofinteres00home |url-access=registration |access-date=2008-10-27 }}

{{Debt}}
{{economics}}
{{United States – Commonwealth of Nations recessions}}
{{Authority control}}

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[[Category:Interest rates| ]]
[[Category:Mathematical finance]]
[[Category:Monetary policy]]